Even as they built majorities for trade deals, lawmakers have shown no signs of agreement on cutting the federal deficit. A so-called supercommittee is charged with finding $1.2 trillion in cuts by Thanksgiving. With the deadline looming, a branch of mathematics called game theory may help us understand what happens next.

Here's Robert Smith of NPR's Planet Money team.

ROBERT SMITH, BYLINE: If you've ever thought that politicians play games with the economy - well, you're right. Political scientists often use mathematical game theory to describe how Congress works.

So you may watch CSPAN and see Republicans and Democrats fighting over how to handle the deficit. But a game theorist looks at that and sees...

PROFESSOR STEVEN SMITH: The two players play this game of chicken with each other.

R. SMITH: Steven Smith of Washington University says yes, chicken is a technical game theory term.

(SOUNDBITE OF MUSIC)

R. SMITH: I'm sure you remember it from classic movies like "Rebel Without a Cause." The game is traditionally played with two cars driving as fast as they can right toward each other. Or in the case of James Dean in the movie, the two cars are driving toward a cliff.

(SOUNDBITE OF MOVIE, "REBEL WITHOUT A CAUSE")

COREY ALLEN: (As Buzz Gunderson) She signals. We head for the edge. And the first man who jumps is a chicken... All right?

R. SMITH: There are three options in chicken. If you swerve the car or jump out first, then you lose. If I chicken out first, I lose. But if neither driver flinches...

S. SMITH: They both die.

(SOUNDBITE OF SCREAM AND CRASH)

R. SMITH: Now this sounds extreme, but Professor Smith says this is sort of what we saw last summer with the debt ceiling debate. The cliff was the economic precipice of government default. Democrats and Republicans were in the cars. And remember, the winner of a game of chicken is the driver who shows he's willing to take the greatest risk.

S. SMITH: And so in politics, we oftentimes see two sides in a bargaining game showing the same thing, with one party trying to persuade the other party that it's willing to walk away from the table even if that risks disaster.

R. SMITH: In the case of this summer's debt limit game of chicken, both cars swerved. Both sides claimed victory. President Obama got his debt ceiling increase. Republicans prevented tax increases. And this is where the supercommittee came in. Congress changed the stakes of the game.

S. SMITH: This time they've decided to up the ante. They've decided that, not only, you know, will the driver die but the driver and his family is going to die.

R. SMITH: So imagine two cars filled with beautiful children hurtling toward each other. This is the supercommittee. If the Republicans and the Democrats do not agree on at least $1.2 trillion worth of cuts, then there will be automatic cuts: half from the Pentagon, and half from domestic spending.

S. SMITH: The Republicans presumably do not want the defense budget cut. And Democrats don't want the domestic discretionary programs cut. They'll consider this to be such a serious problem that they will work their way through to an agreement.

R. SMITH: Now there's a whole math side of game theory we can't get into here. It involves ranking preferences and figuring out the expected payoff of each action. But when it comes to the supercommittee, we'll make it simple. Republicans and Democrats won't change what they really want.

But if you can make disaster seem more likely with these automatic cuts, then maybe you can make the politicians slow down the cars. You can make compromise seem better than death. And there's another factor in game theory that may bode well for the supercomittee.

CHARLES STEWART: When you get to a small group, dynamics are different.

R. SMITH: Charles Stewart is a political scientist at MIT. He says the fewer number of game players, the simpler the game. The supercomittee has only 12 members of Congress, and so they may play better with others.

STEWART: In their heart of hearts, their preferences might not change, but they are willing to bargain in a different way.

R. SMITH: So the committee is small. The stakes are high. Game theory says this bodes well for compromise. What could possibly go wrong?

(SOUNDBITE OF MUSIC)

R. SMITH: Well here's the final lesson of chicken. One mistake can be disastrous. In "Rebel Without a Cause," one of the drivers gets his sleeve caught in the door. And he goes off the cliff. This is not the way you want to win a game of chicken or politics.

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